BERKELEY, Calif. (AP) — Big Tech companies that operate around the globe have long promised to obey local laws and to protect civil rights while doing business. But when Apple and Google capitulated to Russian demands and removed a political-opposition app from their local app stores, it raised worries that two of the world's most successful companies are more comfortable bowing to undemocratic edicts — and maintaining a steady flow of profits — than upholding the rights of their users.

The app in question, called Smart Voting, was a tool for organizing opposition to Russia President Vladimir...